Tableau formulas for skew Grothendieck polynomials

TL;DR

This paper develops tableau formulas for skew Grothendieck polynomials across all four classical Lie types, providing combinatorial tools for their computation and understanding.

Contribution

It introduces set-valued tableaux for skew elements and derives explicit tableau formulas for skew Grothendieck polynomials in all classical types.

Findings

Tableau formulas for skew double Grothendieck polynomials

Explicit formulas for Grassmannian Grothendieck polynomials

K-theoretic analogues of skew Stanley functions

Abstract

An element of a Weyl group of classical type is skew if it is the left factor in a reduced factorization of a Grassmannian element. The skew Grothendieck polynomials are those which are indexed by skew elements of the Weyl group. We define set-valued tableaux which are fillings of the associated skew Young diagrams and use them to prove tableau formulas for the skew double Grothendieck polynomials in all four classical Lie types. We deduce tableau formulas for the Grassmannian Grothendieck polynomials and the K-theoretic analogues of the (double mixed) skew Stanley functions in the respective Lie types.